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(didn't watch youtube link)
How 'bout adding no weight at all? Just need a heat sealer (I've purchased 'em used for $30 or so):
1) Placing the cut bag (=tube element) inside the end bag;
2) With edges even with each other;
3) Use impulse sealer (=industrial heat sealer) to seal exposed ends;
4) Roll bag assembly towards or away from you until you've sealed the whole circumference;
5) Pull the cut bag (=tube element) out of end bag, leaving the sealed edges sticking outwards (trim them with scissors if desired);
6) Add the next cut bag (=tube element) and repeat;
7) Continue 'til last bag: use the end bag rather than a cut bag (tube element) stuffed into the assembled long tube, with edges aligned.
Might be a bit rough, as the 'bite' of the impulse sealer will be more like a series of scallops as you twiddle the bag (you can't seal continuous lines longer than the unit's size, so you have to lay just that length into the sealer, then move along). But it would probably be doable. Will try and post results... in my spare time...
Thanks for the fun idea!
.
Doing the math: Let's assume the air inside the bag is going to get 25 degrees hotter than outside. I'll measure it if I try this project, but let's just throw some numbers around. (I chose 25 for a reason: stick with me.) A change of 25 degrees F = a change of about 14 degrees C (C=F*5/9, ignoring the 32 degree fudge since it's a difference we're talking about); this is also the change in degrees Kelvin, since the C and K degrees are the same size.
PV=nRT is the universal gas formula where P=pressure, V=volume, n=number of molecules, R=gas constant, and T=temperature in degrees Kelvin
P you want the same (see above); n and R don't change, so what you get is: V=fT (f being a fudge factor), so
V1=fT1 and V2=fT2
Solve for f: f=V1/T1 and f=V2/T2
Combine the two: V1/T1 = V2/T2
Collect Volumes on one side an Temps on the other: V2/V1 = T2/T1
Thus the percent change in volume (V2/V1) is proportional to the change in temperature (T2/T1) ...which you knew: hotter = bigger
But what is the percent change in temp? Thus, if T goes up by 25 degrees F = 14 degrees Kelvin (from the wild guess, above), it's going from about 300K to 314K, or a change of about 5%. (This assumes that it is 80 degrees outside.)
So, if one UNDERFILLS the bag by five percent, it will inflate completely and to neutral pressure when it warms to 105 degrees F.
To do this one would measure the bag length in inches and multiply that by 0.05, and roll up that length of plastic at the end and put some books or a board on it, fill to desired plumpness, seal, then remove the weight and let the bag slump a bit. For a ten-foot-long balloon that would come to six inches rolled up before inflating.
I think. It's 3:41 AM...